Periodic dynamics in Daphnia populations: Biological interactions and external forcing

Populations of the freshwater crustacean Daphnia were grown in laboratory microcosms for nearly 2 yr, to assess periodicity and other features of population dynamics. Two experimental manipulations were imposed: the addition of other crustacean species and imposition of externally forced temperature variations. Linear time series analysis revealed cyclic dynamics, with periods ranging from 41 to 182 d. Periodic behavior was qualitatively robust to both experimental manipulations. It occurred in populations of D. pulicaria in microcosms with and without additional species of crustaceans, and it occurred in populations of D. magna with and without externally imposed oscillations in temperature. Periodicity was observed both in populations that persisted and in those that went extinct during the experiment. The experimental treatment of additional crustacean species, and perhaps that of temperature forcing, reduced the period of oscillation. For the longest time series, nonlinear autoregression techniques gave negative Lyapunov exponents, consistent with stable but noisy periodic dynamics rather than chaotic dynamics. Periodic models with a single fundamental frequency typically did not capture all the periodic behavior, however, suggesting that additional frequencies or responses to demographic stochasticity were present.